Ostrogradsky instability
In applied mathematics, the Ostrogradsky instability is a consequence of a theorem of Mikhail Ostrogradsky in classical mechanics according to which a non-degenerate Lagrangian dependent on time derivatives higher than the first corresponds to a linearly unstable Hamiltonian associated with the Lagrangian via a Legendre transform. The Ostrogradsky instability has been proposed as an explanation as to why no differential equations of higher order than two appear to describe physical phenomena.
